7etf be antinuous and differentiable on an intervalI Let XoE I, Prove that For Guchat x th EI, there ext ECO1) such tuat f(x) -hf(X,thQ). Hint; Apply the MUT to 9:L6,1]IR any HEIR O = , %3D

Q: Q Find the derivativeof y)with respect tox; in the foltowina function s and u=3X 2 Find dy for the…

A: Given that  The functions  As for the guide lines to solve the one question but here I am solving…

Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: Suppose f:R→IR is a diffexetiuble function which satısfies flo) = 0 . We wort to shouw f': IR → IR…

A: We have to do implicit differentiation.

Q: 3) Let PIASR ond Thi AxC ßeD. Then his a Anction. Te Ø # 4 B and ø 7b cD then that h'(Y x Y% ]=…

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Q: 3. y" +y = 2 cos x - sin x; y = x sin x+ x cos x

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Q: 1. Find if the function is continuous in the given points (sin(x+y) x+y 1 D) f(x, y) = x + y = 0…

A:

Q: 2. ASSUME f(x) IS CONTINUOUS AND DIFFERENTIABLE ON AN OPEN INTERVAL AS GRAPHED. WHICH OF THESE…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Given the graphs of f(x), f'tx)and frx) determine x-coordinates of the points O 8, c,'D, E O show…

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Q: Use Mean value theorem to show that (1+ x)' 2 (1+2x).x21.

A: Mean value theorem: Let f be a continuous function on the closed interval a, b and differentiable on…

Q: 3) Consider The functjun fle) = G-a)? (x-1) A Find the Pointts q Inflection (1ist this as (x, y)…

A: Given, the function fx=x-23x-1. We have to answer the following...

Q: use the definition to find the derivetive of feconction fcx) = 「X+/ and obtain Hりe equabion of ナんe…

A:

Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: a) Find the intervals on which f is increasing b) Find the intervals on which f is decreasing c) The…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: True/False; f (x) =; 1 is continuous on 2х —1 A) False B) True If f(-3)=6, f(2)= and f is continuous…

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Q: Find he derivative Of the funchon f by using the cules of di ecentation fo) 32x²-42c²t4

A: Given, f(x)=2x3-4x2+4The derivative of fx with respect to x is defined as:limh→0fx+h−fxh

Q: Theorem 1 (For open convex domain). Suppose 2 is a convex open set. Let f be analytic in 2 \{a} and…

A: We can break the integrand {\displaystyle f}, as well as the differential {\displaystyle dz}…

Q: Dw many critical points does the fu

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Q: what type of a calculus calculation is this?

A:

Q: Explain why or why not Determine whether the following statements are true and give an explanation…

A: We have to determine whether the given statements are true or not: a.  ∫fx f'x dx=12fx2+Cb.  ∫fxn…

Q: o let fon= (x-1)? +2; xzl a find f-(x),domain range b) confirm fof cigraph t Uning yix using…

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Q: Observe that the function is continuous at each member of its domain. State the domain as an…

A:

Q: Show that f is continuous on (-0,00) sin x if x 4 V

A:

Q: 24: Prove that: secx * cscx = tan x + cot x

A: To prove the given identity

Q: HW/ Prove that: (1) 1-tanif x sechx

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Q: Let/(x)=sin³ x+A sin² X

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Q: prove that f(x) = x sin√x is not [0,00) uniformly Continums

A: fx=xsinx We have to show fx is not uniformly continuous on [0,∞)

Q: Theorom:- Let f-3GDCI); XoEIthen O TfaeR then a fisdefferantible at (a P) (xo)= QP(xo) D ft…

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Q: f sint dt Evaluate lim

A: We will use DL hospital rule and Newton leibniz formula to solve this question.

Q: real mummber tzo ) if fex)= 20Vř, Show that for any f (t x) = VE +(a) 2) Consider the function fx)=…

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Q: Suppose fis a real valued function defined on an open interval I and differentiable at every x eI.…

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Q: tinuous, prove that T/2 T/2 f(cos x) dx = f(sin x) dx (b) Use part (a) to evaluate /2 cos?x dx and…

A:

Q: Problem 4. Let LC R³ be the lower hemispherc, i.c. FOLLO ALLE = {(x, y, z) | x² + y² + z² = 1 and z≤…

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Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.